The win was Pools' sixth in seven games and their third in a row at Victoria Park but it was tough going at times against an in-form Daggers, with just one loss in nine.
Andy Monkhouse won it for the home side with a 79th-minute header from Matty Dolan's corner, in a game that was in the balance for a long time.
Cooper admitted: "It's very satisfying as I thought it was going away from us.
"Speaking to Wayne (Burnett, Dagenham boss) after the game, Dagenham deserve a lot of credit for the way they came here and played.
"Our work-rate was high - it's a cornerstone of any performance. We started at a nice tempo and we had to try and get forward through the opposition and we did well.
"We wanted to kick on, but they came back at us. We have ground that out and our 'keeper has made some terrific saves."
Pools took the lead after 15 minutes when Luke James knocked the ball across goal for James Poole to knock in from close range for his fourth of the season.
But they were pegged back by the visitors, with home goalkeeper Scott Flinders making a number of fine saves.
"Maybe we have ridden it a little bit, but we created a chance to win the game," added Cooper.
"I think Dagenham were as good as we have played at home this season, so I'm very pleased to win it.
"We played some really nice football at times, be progressive, score goals, and my team here to a man have really dug in to make sure we had an opportunity to win the game and thankfully we have done it."